Numerical study of the coupled Burger and Burger Huxley equations using Bessel collocation scheme

Abstract

Bessel collocation method (BCM) has been presented to solve the system of coupled nonlinear Burger and Burger Huxley equations. Spherical Bessel functions of first kind J_n(x) have been used as base functions in space direction to discretize the problem. Study of Hypergeometric representation of Bessel polynomial have also been focused. The convergence of the technique has been discussed through weighted norm inequalities. L₂-norm and L_? -norm have been calculated to study the error analysis. Bessel collocation has been applied on five coupled nonlinear partial differential equations to check its effectiveness. Numerical values have been compared at different number of collocation points, to the exact values and values reported in the literature to check the applicability of the technique. The system of equations has been presented in block matrix structure. The system of equations, after discretization have been solved by using Matlab. Results obtained from BCM have also been discussed in graphical form via surface plots.